blockchain would allow: - trustless cloud-based indexed storage of encrypted data using protocols such as IPFS - logging of data access requests to a globally accessible database and ability to give and remove permissions based on timestamps - auditing of data accessors to ensure that their access patterns match their functions - eg. if a hospital suddenly starts trying to download data on a million patients instead of 300 then this would be visible on the blockchain and individuals could then question why this is occurring and prevent access.

All of these things can be done with trusted intermediaries, but when you start considering use cases such as - being in china and needing to allow a chinese hospital to access your records back in the USA, suddenly these things become important.